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This paper develops a scattering theory for the asymmetric transport observed at interfaces separating two-dimensional topological insulators. Starting from the spectral decomposition of an unperturbed interface Hamiltonian, we present a…

Spectral Theory · Mathematics 2025-08-13 Binglu Chen , Guillaume Bal

Active matter encompasses different nonequilibrium systems in which individual constituents convert energy into non-conservative forces or motion at the microscale. This review provides an elementary introduction to the role of topology in…

Soft Condensed Matter · Physics 2022-06-28 Suraj Shankar , Anton Souslov , Mark J. Bowick , M. Cristina Marchetti , Vincenzo Vitelli

Topological insulators are unique physical structures that are insulators in their bulk, but support currents at their edges which can be unidirectional and topologically protected from scattering on disorder and inhomogeneities. Photonic…

Two-dimensional topological insulator features time-reversal-invariant spin-momentum-locked one-dimensional (1D) edge states with a linear energy dispersion. However, experimental access to 1D edge states is still of great challenge and…

While the experimental progress on three dimensional topological insulators is rapid, the development of their two dimensional counterparts has been comparatively slow, despite their technological promise. The main reason is materials…

Mesoscale and Nanoscale Physics · Physics 2015-06-10 M. Kindermann

Topological Anderson insulators represent a class of disorder-induced, nontrivial topological states of matter. In this study, we propose a feasible strategy to unveil and design topological Anderson insulators protected by latent…

Disordered Systems and Neural Networks · Physics 2026-03-05 Jing-Run Lin , Shuo Wang , Hui Li , Zheng-Wei Zuo

In the research of the topological band phases, the conventional wisdom is to start from the crystalline translational symmetry systems. Nevertheless, the translational symmetry is not always a necessary condition for the energy bands. Here…

Disordered Systems and Neural Networks · Physics 2025-12-03 Shuo Wang , Jing-Run Lin , Zheng-Wei Zuo

Recent theories and experiments have suggested that strong spin-orbit coupling effects in certain band insulators can give rise to a new phase of quantum matter, the so-called topological insulator, which can show macroscopic entanglement…

Mesoscale and Nanoscale Physics · Physics 2009-08-26 Y. Xia , D. Qian , D. Hsieh , L. Wray , A. Pal , H. Lin , A. Bansil , D. Grauer , Y. S. Hor , R. J. Cava , M. Z. Hasan

A central property of (Chern) topological insulators is the presence of robust asymmetric transport along interfaces separating two-dimensional insulating materials in different topological phases. A Topological Anderson Insulator is an…

Analysis of PDEs · Mathematics 2023-11-28 Guillaume Bal , Thuyen Dang

Disorder, ubiquitously present in solids, is normally detrimental to the stability of ordered states of matter. In this letter we demonstrate that not only is the physics of a strong topological insulator robust to disorder but, remarkably,…

Mesoscale and Nanoscale Physics · Physics 2010-12-03 H. -M. Guo , G. Rosenberg , G. Refael , M. Franz

Strong disorder drives conventional Hermitian systems into Anderson insulating states, suppressing all topological phases. Here, we unveil symmetry-protected, anomalous topological phases in the strong disorder limit of a non-Hermitian…

Mesoscale and Nanoscale Physics · Physics 2026-02-11 Mina Ren , Xi Shi , Haitao Jiang , Feng Liu , Hong Chen , Yong Sun

One-way edge states at the surface of photonic topological insulators are of significant interest for communications, nonlinear and quantum optics. Moreover, when reciprocity is broken in a photonic topological insulator, these states…

Optics · Physics 2018-10-17 Momchil Minkov , Shanhui Fan

Topological materials exhibit edge-localized scattering-free modes protected by their nontrivial bulk topology through the bulk-edge correspondence in Hermitian systems. While topological phenomena have recently been much investigated in…

Mesoscale and Nanoscale Physics · Physics 2020-11-16 Kazuki Sone , Yuto Ashida , Takahiro Sagawa

Topological states of quantum matter exhibit unique disorder-immune surface states protected by underlying nontrivial topological invariants of the bulk. Such immunity from backscattering makes topological surface or edge states ideal…

Mesoscale and Nanoscale Physics · Physics 2015-11-09 S. Hossein Mousavi , Alexander B. Khanikaev , Zheng Wang

We study surface states of topological crystalline insulators and superconductors protected by inversion symmetry. These fall into the category of "higher-order" topological insulators and superconductors which possess surface states that…

Mesoscale and Nanoscale Physics · Physics 2018-05-30 Eslam Khalaf

We investigate the scattering and localization properties of edge and bulk states in a disordered two-dimensional topological insulator when they coexist at the same fermi energy. Due to edge-bulk backscattering (which is not prohibited…

Mesoscale and Nanoscale Physics · Physics 2014-08-26 Yan-Yang Zhang , Man Shen , Xing-Tao An , Qing-Feng Sun , Xin-Cheng Xie , Kai Chang , Shu-Shen Li

The robust transport of edge modes is perhaps the most useful property of topological materials. The existence of edge modes is guaranteed by the bulk-edge correspondence, which states that the number of topological edge modes is determined…

Mesoscale and Nanoscale Physics · Physics 2022-10-26 Mudi Wang , Qiyun Ma , Shan Liu , Ruo-Yang Zhang , Lei Zhang , Manzhu Ke , Zhengyou Liu , C. T. Chan

Topological crystalline insulators are a class of materials with a bulk energy gap and edge or surface modes, which are protected by crystalline symmetry, at their boundaries. They have been realized in electronic systems: in particular, in…

Mesoscale and Nanoscale Physics · Physics 2016-10-25 Jian-Xiao Zhang , Mikael C. Rechtsman , Chao-Xing Liu

Insulating materials with dynamical spin degrees of freedom have recently emerged as viable conduits for spin flows. Transport phenomena harbored therein are, however, turning out to be much richer than initially envisioned. In particular,…

Mesoscale and Nanoscale Physics · Physics 2018-12-05 Yaroslav Tserkovnyak

Photonic topological insulators (PTIs) exhibit robust photonic edge states protected by band topology, similar to electronic edge states in topological band insulators. Standard band theory does not apply to amorphous phases of matter,…